Reduced order modeling in FDTD with provable stability beyond the CFL limit

Abstract

The Finite-Difference Time-Domain (FDTD) method is widely used in signal and power integrity, applied electromagnetism, and physics. Unfortunately, its computational efficiency can be severely degraded for multiscale problems, where small and large features coexist. This scenario is common in signal and power integrity, because of the large aspect ratio of interconnects and power/ground planes. In this paper, we show how multiscale FDTD simulations can be accelerated with model order reduction. A detailed model for complex objects is first generated using a fine FDTD grid. The model is then compressed with model order reduction, and embedded into a main coarse grid. During this process, the stability limit of the reduced model can be also extended, enabling the use of a larger time step in the whole domain. Using a passivity argument, we are able to systematically guarantee the stability of the resulting scheme, which is a main novelty with respect to previous works. A numerical example with two reduced models shows the potential of the proposed ideas.